MATH 597/GEOPH 697 Fall 2004





HOMEWORK DUE THURSDAY OCTOBER 21:
The following three questions:





  1. Transform the two-dimensional form of the Navier Stokes equations by using the following non dimensional variables:

    \begin{eqnarray*} t^*=t\frac{U_0}{L} & \displaystyle x^*=\frac{x}{L} & u^*=\fra... ...isplaystyle y^*=\frac{y}{\epsilon L} & v^*=\frac{v}{\epsilon U_0}\end{eqnarray*}


    where $\displaystyle \epsilon = \frac{1}{\sqrt{R}}=\sqrt{\frac{\nu } {U_0 L}} $. Show that the non dimensional Navier-Stokes equations have different solutions for different values of $\epsilon $.
  2. Transform the boundary layer equations using the same non dimensional variables and show that they do not explicitly depend on $\epsilon $.
  3. Explain physically why the non dimensional Navier-Stokes equations depend on the Reynolds number $R$, while the boundary layer equations do not.